In pure JSF app JSF's UI component tree would be in session. However in Seam there is a concept ofconversation and (I believe) in different conversations UI tree could be different. Does it mean Seam would store UI tree in conversation context?

Seam does not manage the ui component tree. The actual component tree scope is request. In the end of the request the tree state is serialized and kept in the session and the state is restored on postback.